Joint universality of periodic zeta-functions with multiplicative coefficients. II - Laurinčikas, Antanas; Šiaučiūnas, Darius; Tekorė, Monika (Nonlinear Analysis: Modelling and Control, 2021)
In the paper, a joint discrete universality theorem for periodic zeta-functions with multiplicative coefficients on the approximation of analytic functions by shifts involving the sequence f kg of imaginary parts of nontrivial zeros of the Riemann zeta-function is obtained. For its proof, a weak form of the Montgomery pair correlation conjecture is used. The paper is a continuation of [A. Laurinčikas, M. Tekorė, Joint universality of periodic zeta-functions with multiplicative coefficients, Nonlinear Anal. Model. Control, 25(5):860–883, 2020] using nonlinear shifts for approximation of analytic functions.
Keywords: joint universality; nontrivial zeros of the Riemann zeta-function; periodic zeta-function; space of analytic functions; weak convergence